Supernovae of type IIP are marked by the long plateau seen in their optical light curves. The plateau is believed to be the result of a recombination wave that propagates through the outflowing massive hydrogen envelope. Here, we analytically investigate the transition from a fully ionized envelope to a partially recombined one and its effects on the SN light curve. The motivation is to establish the underlying processes which dominate the evolution at late times when recombination takes place in the envelope, yet early enough so that $^{56}$Ni decay is a negligible source of energy. We assume a simple, yet adequate, hydrodynamic profile of the envelope and study the mechanisms which dominate the energy emission and the observed temperature. We consider the diffusion of photons through the envelope while analyzing the ionization fraction and the coupling between radiation and gas. We find that once recombination starts, the observed temperature decreases slowly in time. However, in a typical red supergiant (RSG) explosion, the recombination wave does not affect the bolometric luminosity immediately. Only at later times, the cooling wave may reach layers that are deep enough to affect the luminosity. We find that the plateau is not a generic result of a recombination process in expanding gas. Instead it depends on the density profile of the parts of the envelope which undergo recombination. Our results are useful to investigate the light curves of RSG explosions. We show the resulting light curves of two examples of RSG explosions according to our model and discuss their compatibility with observations. In addition, we improve the analytical relations between the plateau luminosity and plateau duration to the properties of the pre-explosion progenitor (Arnett 1980; Popov 1993).
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